Question

If 1/4x - 1 ≤ -x 5, what is the greatest possible value of x?

a) -1
b) 1
c) 4
d) 5

Answer 1

To find the greatest possible value of x in the inequality 1/4x - 1 ≤ -5x, after simplification, x must be less than or equal to 4/21. Since this value is not among the options provided, the correct answer is 'None of the above'.

Step-by-step explanation:

The student is asking to solve an inequality involving a variable x. To find the greatest possible value of x that satisfies the inequality 1/4x - 1 ≤ -5x, one must first combine like terms and isolate the variable.

1. First, add 5x to both sides of the inequality to get 1/4x + 5x ≤ 1.
2. Combine the x terms by finding a common denominator, which leads to (1+20)/4x ≤ 1.
3. Simplify to get 21/4x ≤ 1.
4. Multiply both sides by 4/21 to isolate x and get x ≤ 4/21.

Since 4/21 is less than 1, the greatest possible integer value for x is 0. However, this does not match any of the options provided: -1, 1, 4, 5. Therefore, the correct answer is d. None of the above.